Challenging Problems on the Topic of Pythagorean Theorem

You are encouraged to try out these challenging problems to enrich and extend your knowledge of this topic beyond the basic. One Bunus Mark will be awarded for each mathematically correct and clearly presented solution.

1)

2)

3)

4)

5)

6) “How far is the Horizon?” Problem

Suppose the Earth is an ideal sphere with the radius of 6370 km. How far would you be able to see from a position with a height of:

7) Some magpies are nesting at the top of two trees which stand 25 m apart. The two trees are 12 m and 8 m tall. Jane made a birdfeeder for the young magpies. Her brother Kevin installed it on a 3.5 metre tall pole. Where did the two children plant the birdfeeder into the ground so that the young birds from both nests have an equal distance to the birdfeeder?